## vector dot product help.

i have three vectors: a=4,b=3,c=5 that form a right triangle.
vector a is in the positive x direction, vector b is in the positive y direction starting at the tip of a. vector c is the hypotenuse of the triangle with tip at the origin. (see attaced picture .doc file)

the questions are: what is a dot b, a dot c, and b dot c.

i have the solutions in my manual but i dont understand them.

the manual says that from the figure it is clear that a + b + c = 0, where a is perpindicular to b:

a dot b = 0, since the angle between them is 90 degrees:

a dot c = a dot (-a-b)=-|a|^2=-16

and similarly b dot c = -9

i have no idea whay this is true. any help would be appreciated especially a general explanition of what the dot product is
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 Blog Entries: 9 Recognitions: Homework Help Science Advisor Is that a joke...?You posted only 2... Daniel.
 Recognitions: Gold Member A dot product between vector a and vector b is this: a dot b = |a|*|b|*cos(theta) a dot b = (AxBx)i + (AyBy)j + (AzBz)k Those are two definitions and they are equal. In your case, you are given the lenght of vectors (a=4,b=3,c=5). This is the called the magnitude of a vector. the |a| = 4, |b| = 3, |c| = 5. How would you find the angle theta between the two vectors? There are two laws you can use. Law of sines and law of cosines. Or a pythogoras' theorem if the vectors form a right angle. In your case the triangle is right, because 4^2 + 3^2 = 5^2. So you can use a good old SOH CAH TOA rule (Sin = Opposite/Hypothenus, Cos = Adjacent/Hypothenus, Tan = Opposite/Adjecent). Try to visualize the triangle first. Obviously c is a hypothenus with lenght 5. This is given: |a| = 4, |b| = 3, |c| = 5 And you want to find: 1] a dot b = |a|*|b|*cos(theta)= 4*3*cos(90) = 0 2] a dot c = |a|*|c|*cos(theta) = 4*5*4/5 = 16 3] b dot c = |b|*|c|*cos(theta) = 3*5*3/5 = 9

## vector dot product help.

ok i made my mistake with soh cah toa , but the last two answers are -16 and -9. why the negative sign? thx

Mentor
Blog Entries: 1
 Quote by RadiationX why the negative sign?
Because the angle between the vectors ($\theta$) is 90 < $\theta$ < 180 degrees, a region in which $cos \theta$ is negative.

 Quote by Doc Al Because the angle between the vectors ($\theta$) is 90 < $\theta$ < 180 degrees, a region in which $cos \theta$ is negative.

i'm not saying that your're wrong but how do you know that cos is in the second quad? from the picture this is not obvious.
 Mentor Blog Entries: 1 To find the angle between two vectors, redraw them so that their tails start at the same point. Direction matters!
 that's it!!! thank you Doc AI

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